reserve m,n for Nat;
reserve r for Real;
reserve c for Element of F_Complex;

theorem Th26:
  c is algebraic iff
  ex f being non-zero INT -valued Polynomial of F_Complex st c is_a_root_of f
  proof
    hereby
      assume c is algebraic;
      then ex f being monic RAT-valued Polynomial of FC
      st c is_a_root_of f by Th25;
      hence
      ex f being non-zero INT -valued Polynomial of FC st c is_a_root_of f
      by Th24;
    end;
    assume
    ex f being non-zero INT -valued Polynomial of FC st c is_a_root_of f;
    then ex f being monic RAT-valued Polynomial of FC
    st c is_a_root_of f by Th24;
    hence thesis by Th25;
  end;
